Question

If two positive integer m and n are expressed in the form m=pq³ and n =p³q³, whether p and q are prime numbe ,find lcm(m,n) and HCF(m,n)

Answer 1

Step-by-step explanation:

Given -

• Two positive integers m and n are expressed in the form m = pq³ and n = p³q³, where p and q are prime numbers

To Find -

• LCM(m,n) and HCF(m,n)

Now,

• pq³ = p × q × q × q
• p³q³ = p × p × p × q × q × q

HCF(m,n) = pq³

LCM(m,n) = p³q³

Verification :-

• LCM × HCF = product of two numbers

→ pq³ × p³q³ = pq³ × p³q³

→ p^4q^6 = p^4q^6

LHS = RHS

Hence,

Verified..

It shows that our answer is absolutely correct.

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ HCF(m, n) = pq³

$\implies$LCM(m, n) = p³q³

$\large\underline\mathrm{Given:-}$

• two positive integer m and n are expressed in the form m = pq³ and n = p³q³, whether p and q are prime numbers.

$\large\underline\mathrm{To \: find}$

• HCF(m, n) and LCM(m, n)

$\large\underline\mathrm{Solution}$

$\implies$ pq³ = p × q × q × q

$\implies$ p³q³ = p × p × p × q × q × q

$\implies$ HCF(m, n) = pq³

$\implies$ LCM(m, n) = p³q³

$\large\underline\mathrm{Verification}$

$\large\underline\mathrm{HCF \: × \: LCM \: = \: product \: of \: two \: number}$

$\implies$ pq³ × p³q³ = pq³ × p³q³

$\implies$p^4q^6 = p^4q^6

$\large\underline\mathrm{LHS = RHS}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$